When inflationary perturbations refuse to classicalise: the role of non-Gaussianity in Wigner negativity

TL;DR

This paper investigates whether quantum features of inflationary perturbations, specifically non-Gaussianity and Wigner function negativity, persist on large scales, challenging the assumption that such perturbations become classical after inflation.

Contribution

The study computes the Wigner function of curvature perturbations with non-Gaussianities in the EFT of inflation, revealing persistent quantum interference effects on super-Hubble scales.

Findings

Wigner function develops interference fringes on super-Hubble scales.

Negativity of the Wigner function grows as the scale factor squared in ultra-slow-roll backgrounds.

Quantum effects can remain significant at late times, challenging classicality assumptions.

Abstract

Inflationary perturbations are quantum in origin. Yet, when computing cosmological observables, they are often treated as classical stochastic fields. Do they nevertheless retain quantum birthmarks? A hallmark of genuinely quantum behaviour is quantum interferences, arising from phase coherence between distinct branches of the wavefunction. Such interference is diagnosed by the non-positivity of the Wigner function, and according to Hudson's theorem, the only pure states with positive Wigner functions are Gaussian states. Consequently, any departure from Gaussianity necessarily implies a non-positive Wigner function, precluding a description in terms of a classical distribution. This motivates us to compute the Wigner function of curvature perturbations, accounting for primordial non-Gaussianities, using the EFT of inflation. We find that the Wigner function develops pronounced interference fringes on super-Hubble scales, and in particular, its negativity grows as $a^2$ in ultra-slow-roll backgrounds. These results demonstrate that quantum effects can remain significant at late times, and that squeezing alone does not ensure classicality, contrary to standard lore. This suggests that the prospects for detecting genuinely quantum signatures of the universe's origins in cosmological observables may be less bleak than previously thought.